At Asiacrypt 2009, Kurosawa and Nojima showed a fully simulatable adaptive oblivious transfer (OT) protocol under the DDH assumption in the standard model. However, Green and Hohenberger pointed out
that the communication cost of each transfer phase is O(n), where n is the number of the sender's messages. In this paper, we show that the cost can be reduced to O(1) by utilizing a verifiable shuffle protocol.